Can I attach a new internet router to an att uverse router?

[Nick]

So I'm on att uverse and there is no possible way of switching since we use it for all our tvs and home phones. I was wondering if I could purchase a router with good speeds of up/down and some how plug it into my att router. Is this going to cost me extra money to plug it in? Is this idea even possible? Should I just purchase a separate internet line? Any ideas?